System of Equations : Money

Damian has been saving coins he finds on the ground for several months. So far he has found 37 coins that are either pennies or nickels. The combined value of his found pennies and nickels currently is $1.09. What is the system of linear equations, written using standard form, represents the situation if Damian found p pennies and n nickels.​

Answers

Answer 1

Answer:

18 nickles 19 pennies

Step-by-step explanation:

value of 1 penny=$0.01

value of 1 nickle=$0.05

0.01p+0.05n=1.09

p+n=37

there are two methods for this system

I.substitution

p+n=37

p=37-n

we replace p in the first relation

0.01(37-n)+0.05n=1.09

0.37-0.01n+0.05n=1.09

0.04n=0.72

n=18 nickels

p+18=37

p=37-18=19 pennies

II.reduction

0.01p+0.05n=1.09

p+n=37

we multiply the second equation by 100

p+5n=109

p+n=37

we calculate the difference between the two relations

p-p+5n-n=109-37

4n=72

n=18

p+18=37

p=19


Related Questions

Two bags of cereal are packed in a box. The total weight of the box and the two bags of cereal is 50.00 ounces. One bag of cereal weighs 16.03 ounces, the other weighs 18.98 ounces. How much does the box weigh?
14.99 ounces
14.72 ounces
14.08 ounces
14.01 ounces

Answers

14.99 is the correct answer

what is 0.47 of £1 as pound sign

Answers

Answer:

In the Unicode standard, the symbol £ is called POUND SIGN, and the symbol ₤ is the LIRA SIGN.

Suppose you have a $15 coupon that can be used on any purchase over $100 at your favorite clothing store. The discounted price of a sports jacket is $203. What is the retail price of the jacket?
a.
$235.70
b.
$303.00
c.
$188.00
d.
$218.00

Answers

the answer is C , $188.00 have a good day

Solve to find X. 3 ≥ -3x

Answers

Answer:

-1 ≤ x

Step-by-step explanation:

You just need to divide -3 on both sides.

-1 ≤ x

Note that since you are dividing by a negative number, the sign flips.

-1 ≤ x

Step-by-step explanation:

First start with the equation:

3 ≥ -3x

divide by -3 to get x positive and singular:

-1 ≥ x

and since we divided by a negative we need to flip the sign:

-1 ≤ x  would be your answer

hope this helped :)

The random variable X has mean 12 and standard deviation 3. The random variable W is defined as W = 7+2X. What are the mean and standard deviation of W?
A. The mean is 24, and the standard deviation is 6.
B. The mean is 24, and the standard deviation is 13.
C. The mean is 31, and the standard deviation is 3.
D. The mean is 31, and the standard deviation is 6.
E. The mean is 31, and the standard deviation is 13.

Answers

Answer: D. The mean is 31, and the standard deviation is 6.

Step-by-step explanation:

Given the data :

X = mean = 12 ; Standard deviation = 3

W = 7 + 2x

Variance of W = 2x

Variance = Standard deviation²

(2x)² = 4x²

Variance

Standard deviation of X = 3

Variance (W) = 4*3² = 4 * 9 = 36

Variance (W) = 36

Standard deviation = sqrt(variance)

Standard deviation = sqrt(36) = 6

Mean ; of x = 12

Mean(W) = 7 + 2(12)

Mean = 7 + 24

Mean = 31

What is the area trapezoid ABCD A(-1,5) B(3,2) C(0,-2) D(-13,-11)

Answers

Answer:

62.5

Step-by-step explanation:

slope of AB = (5-2)/(-1 - 3) = -3/4

slope of BC = (2 - -2)/(3-0) = 4/3

AB ⊥ BC  (slope -3/4 vs 4/3)

seg AB = √(-1 - 3)² + (5 - 2)² = √25 = 5

seg BC = √(3 - 0)² + (2 - -2)² = √25 = 5

seg AD = √(-1 - -13)² + (5 - -11)² = √400 = 20

Area   (BC + AD) * AB / 2 = (5 + 20) * 5 / 2 = 62.5

please help. im pretty stumped

Answers

Answer:

-

you write the answer here

Step-by-step explanation:

and explain here

2(5x+7)=16
what the answer?

Answers

Answer:

x = 1/5

Step-by-step explanation:

2(5x + 7) = 16

2 * 5x + 2 * 7 = 16

10x + 14 = 16

10x = 16 - 14

10x = 2

x = 2/10

x = 1/5

Solve 3x − 5y = 17
9x − 15y = −4

Answers

Answer:

3x - 5y = 17

3(9) - 5(2) = 17

27 - 10 = 17

x = 9

y = 2

---------------------

9x - 15y = -4

I believe this equation has no proper solution. Every "solution" I have found ends with repeating decimals & fractions.

Solve the following formula for the indicated variable.
– 5x – 3y = 13: solve for y.

Answers

9514 1404 393

Answer:

  y = -5/3x -13/3

Step-by-step explanation:

In any "solve for ..." problem, it is useful to start by identifying where the target is and what has been done to it. Here, y is in one term on the left side of the equation and it has had these things done to it:

multiply by -3add -5x

We want to undo these in reverse order. We undo addition by adding the opposite. We undo multiplication by multiplying by the reciprocal (equivalently, dividing). Whatever we do to one side of the equation, we must also do to the other side.

So, first we add the opposite of -5x to both sides of the equation.

  -5x +5x -3y = 13 +5x

  -3y = 13 +5x . . . . . . . . . collect terms

Next, we undo the multiplication by -3. We can do that by multiplying both sides by 1/(-3) = -1/3.

  (-1/3)(-3y) = (-1/3)(13 +5x)

  y = -5/3x -13/3 . . . . . also we rearranged the terms to standard form

24/7 as a fixed number

Answers

Answer: 24/7 as a mixed number is 3 3/7

Answer:

3 3/7 (mixed number)*

Find the unit rate of 624 calories in 3 servings. Its 8th grade math.

Answers

The answer is 208 calories per serving

Answer:

you can look up the exact quizizz your taking and find all the answers

Step-by-step explanation:

for example: look up your question on the quizizz and then type it in the search bar and add quizziz to the end of it and you should find all your answers there<3

for each one fifth, use a horizontal line or lines to show fractions equivalent to 1/5 and write the equivalent fractions

Answers

Answer:

2/10

Step-by-step explanation:

Find the least common multiple (LCM) of 4 and 5.

Answers

9514 1404 393

Answer:

  20

Step-by-step explanation:

4 and 5 have no common factors*, so their least common multiple is their product:

  4 × 5 = 20

The LCM of 4 and 5 is 20.

_____

* We're concerned with integer factors greater than 1. Of course, 1 is a factor of everything, We could say this as "no common prime factors". For computing the LCM, we really want the GCF (greatest common factor) for use in the formula ...

  LCM(m, n) = mn/GCF(m, n)

The triangles are similar.
What is the value of x?
Enter your answer in the box.
X=

Answers

X=21

If the triangle are similar then you can divide.
75 divided by 25 is 3
72 divided by 21 is 3
so that means if you take 7 times 3 you will get 21
Honestly I don’t even know what this is sorry I tried

Please answer will give brainliest to the best answer please make sure to explain!

Answers

yes he is correct. This is because if you convert all the fractions to be out of 10, the equation is 8/10 minus 5/10 equals 3/10 which is correct. if you have any more questions let me know. i hope this helps :)

Find the volume of the following figure

Answers

Answer:

there is no picture?

Step-by-step explanation:

There is no picture?

due today Solve the equation.

17n=−4

Answers

Answer:

n = -4/17

Step-by-step explanation:

Divide both sides of the equation by the same term

N=-4/17 or -0.2352941176=n

is this right I'm am super confused please help the picture is what I'm saying if you don't under stand

Answers

Answer:

No

Step-by-step explanation:

20/10 = 2/1 (divide top and bottom by 2)

15/30 simplifies to 1/2

(divide top and bottom by 15)

PLEASE HELPPPP ME!!!!!

Answers

Answer:

Problem 1: No

Problem 2: Yes

Step-by-step explanation:

Problem 1:

{(-2, 1), (-2, 3), (0, -3), (1, 4), (3, 1)}

This relation is not a function because there are two y-values, 1 and 3, related to one x-value, -2.

Thus, for a relation to be a function, every x-value must be related to exactly 1 y-value.

Problem 2:

{(0, 2), (3, 4), (-3, -2), (2, 4)}

In this relation, each x-value (domain) has exactly one y-value (range) that it is related to. Therefore, this is a function.

Item 1
One February day, the low temperature in St. Paul, MN was -17°F. Over a period of three hours, the temperature rose 5 °F per hour. After three hours, what was the temperature?
°F

Answers

-2f
5 x 3 is 15, the three stands for the three hours and the five stands for the temperature per hour increase. -17f plus 15 is -2f

Complete the equation.
12 X 4 =
X 2 X4 4

Answers

Answer: 6

Step-by-step explanation: Hope I helped give me a good review and a thanks please

The answer is 6 lov hope this helps

What is the (fg)(x) if
f(x)=(4x - 1) and g(x)=(3x + 5)?
A. 7x + 4
B. 12x2-5
C. 12x2 + 17x-5
D. 12x2 + 23x - 5


Show work

Answers

(4x - 1)(3x + 5)

12x^2 + 20x - 3x -5

12x^2 + 17x -5

The answer is C.

solve ASAP for brain list and thanks make sure it's correct ​

Answers

Answer:

50 C = 122 F

Step-by-step explanation:

50°C × 9/5 +32

Is the point (4,2) a solution of the equation y = 3x - 13?
No
Yes

Answers

No. The point (4,2) is a little off the line.
No ................);&;&($;&?d>,*¥<<£|!€\|¥+

3/16 equals -5/4+ G solve for G

Answers

Answer:

G = 23/16  OR  G = 1.4375

Step-by-step explanation:

3/16 = -5/4 + G

Get the constants on one side. Add 5/4 on both sides.

3/16 + 5/4 = G

To add fractions, find the common denominator. The smallest denominator between these two fractions is 16.

3/16 stays the same since it already has the denominator of 16. To turn the denominator (4) in 5/4 into 16, multiply it by 4. Whatever you do to the denominator, you must do to the numerator.

5 x 4 = 20

The second fraction is now 20/16

3/16 + 20/16 = 23/16

G = 23/16

The answer is : 23/16

Step by step:
3/16= -5/4 + G
3/16+5/4 = 3/16 + 20/16
G= 23/16

200 divided by 60 for example there are 200 milk cartens each one has 60 milk containers how many milk containers exactly are in the cartens

Answers

Answer:

12,000 containers

Step-by-step explanation:

Given : 200 milk cartens are there

60 milk cantainers are there in each cartens.

to find are there in all

200 × 60 = 12,000 containers in all

In rhombus ABCD , m∠EAB=27∘ .

What is m∠EBC ?

Enter your answer in the box.
m∠EBC = °
Rhombus A B C D with diagonals B D and A C intersecting at E.

Answers

Answer:

63°

Step-by-step explanation:

ABCD (rhombus): AC ⊥ BD and bisect at E and same length of 4 sides

∠EBA = 90 - 27 = 63

∠EBC = ∠EAB = 63°

why is it when you take a shower and you come out clean, how does the towel become dirty? This some real mathematics

Answers

okay. so, when you wash your hair, there is no way to get 100% of the shampoo/conditioner out of your hair, so the excess it rubbed onto the towel. Say you have no hair. The shower isn't germ-free, so even if you feel clean, the towel and yourself is still a harbor of germs, good and bad.

-2.5(-3+4n+8)

I need to know fast this is due soon

Answers

Answer:

-10n - 12.5

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Terms/Coefficients/Degrees

Step-by-step explanation:

Step 1: Define

-2.5(-3 + 4n + 8)

Step 2: Simplify

Distribute -2.5:                    7.5 - 10n - 20Combine like terms:           -10n - 12.5
A N S W E R :

For simplifying an expression, there are some rules about the order in which the calculations should be performed. The order of rules is called BODMAS. Each letter in this word stands for an operation.

B = BracketsO = OffD = DivisionM = massA = additionS = substraction

→ -2.5(-3 + 4n + 8) = 0

→ 7.5 + (-10n) + (-20) = 0

→ 7.5 - 10n - 20 = 0

→ -10n - 20 + 7.5 = 0

→ -10n - 12.5 = 0

→ -10n = 12.5

→ n = 12.5 ÷ -10

n = -1.25

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